# Thread: limit definition of derivative

1. ## limit definition of derivative

3)Use the limit definition of derivative and find, $y'$
for $\frac{1}{x+1}$

I know have the answer because we are taught the short cut method in school where we multiply the coefficient by the power and decrease by one. But I want to see how this is done the longer method.

2. Find this limit.
$\displaystyle\lim _{h \to 0} \frac{{\frac{1}
{{x + 1 + h}} - \frac{1}
{{x + 1}}}}
{h}$

3. I end up with:

$\frac{h^2}{(x+1)^2 +h(x+1)}$

4. Originally Posted by elieh
I end up with: $\frac{h^2}{(x+1)^2 +h(x+1)}$
$\dfrac{\frac{1}{x+h+1}-\frac{1}{x+1}}{h}=\dfrac{\frac{(x+1)-(x+h+1)}{(x+h+1)(x+1)}}{h}$
5. $\frac{-h^2}{(x+1)^2 + h(x+1)}$
You said that you already know the answer: $\dfrac{-1}{(x+1)^2}$